A 20-year-old female presents to your emergency service with severe head trauma

Question

A 20-year-old female presents to your emergency service with severe head trauma from a fall. An MRI reveals swelling of her brain, but no sign of hemorrhage. You determine that removing 80 ml of total fluid from her brain will greatly relieve the increasing intracranial pressure. Assuming she was isotonic upon presentation, what osmolarity would you need to achieve in her body to accomplish this? She weighs 70 kg and assume that her brain weighs 1.3 kg and is 70% water. Also, because of the blood brain barrier, treat all of the fluid volume within her cranial cavity as ICF. _____ What volume of 10% mannitol would you need to add to get her to this osmolarity ? The molecular weight of mannitol is 182. _____ Calculate the osmolarity of a 1% glucose solution.

Explanation / Answer

1. The normal Cerebrospinal fluid osmolarity is 300-320 mOsmol/L. therefore, that is the minimum osmolarity is required to achieve isotonic condition in her brain.

2. Osmolarity = Osmoles/ 1000ml

Osmoles = Moles ×Equivalent weight

Osmoles of mannitol = (Mass in Grams ×Numbers of Particles dissociates)/ Molecular Weight       [3]

To achieve 10% mannitol solution we add 10% of total molecular weight of mannitol in grams into 100mL water.

Required weight of mannitol = Molecular Weight× Percentage/ 100 mL

Weight = 182 ×10 / 100 = 18.2g

Now calculate Osmoloes by using formula [3]-

Osmoles of mannitol = (Mass in Grams ×Numbers of Particles dissociates)/ Molecular Weight

= 18.2 ×1/ 182

=0.1 osmoles or 0.1 × 103 mOsmol

= 100 mOsmol

The 10% solution will contain 100 mOsmol in 100 mL of water.

Converting osmolarity in mOsmol/L requires dividing 100 mL by 1 L (1000ml) = [100 mOsmol] / (100mL /1000mL)

= 1000 mOsmol / L

Now to achieve 300 mOsmol/L osmolarity for Cerebrospinal fluid we use following formula.

O1 ×V1 = O2 ×V2 ; here O is osmolarity and V is the volume

Put O1 = 300 mOsmol/L, V1 =1L, O2 = 1000 mOsmol / L and V2 is to calculate

Therefore, 300 × 1 = 1000 × V2

Now, V2 = 300/ 1000 = 0.3mL

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